In: Statistics and Probability
A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 pm lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected and the waiting times are recorded. Suppose that another branch, located in a residential area, is also concerned with the noon-to-1 pm lunch period. A random sample of 15 customers is selected and the waiting times are recorded. Data are available in the worksheet labeled “Problem 3”.
4. Conduct an appropriate test to compare the mean waiting times of the two branches. Report the p-value of this test and state your conclusions.
Data Set
Customer | Waiting Time | Branch |
1 | 4.21 | Residential |
2 | 4.50 | Residential |
3 | 5.55 | Residential |
4 | 6.10 | Residential |
5 | 3.02 | Residential |
6 | 0.38 | Residential |
7 | 5.13 | Residential |
8 | 5.12 | Residential |
9 | 4.77 | Residential |
10 | 6.46 | Residential |
11 | 2.34 | Residential |
12 | 6.19 | Residential |
13 | 3.54 | Residential |
14 | 3.79 | Residential |
15 | 3.20 | Residential |
16 | 9.66 | Commercial |
17 | 10.49 | Commercial |
18 | 5.90 | Commercial |
19 | 6.68 | Commercial |
20 | 8.02 | Commercial |
21 | 5.64 | Commercial |
22 | 5.79 | Commercial |
23 | 4.08 | Commercial |
24 | 8.73 | Commercial |
25 | 6.17 | Commercial |
26 | 3.82 | Commercial |
27 | 9.91 | Commercial |
28 | 8.01 | Commercial |
29 | 5.47 | Commercial |
30 | 8.35 | Commercial |
Here we use two sample t-test to compare the mean waiting times of the two branches.
Testing Hypothesis:
H0 : The mean waiting times of the two branches are equal.
H1 : The mean waiting times of the two branches differ.
Here is the output from Excel :
Here the p-value is 0.00029.
Decision :
Since here p-value < 0.05 , we reject H0 and conclude that the mean waiting times for the two branches are not equal at 5% significance level.